Numerical approach for water distribution system model calibration through incorporation of multiple stochastic prior distributions

Abstract

The use of water distribution system (WDS) hydraulic models facilitates the design and operation of such systems. For offline or online model applications, nodal water demands-variables with the highest levels of uncertainty-should be carefully calibrated because these can considerably affect the accuracy of model outputs in terms of hydraulics and water quality. With the increasing utilization of automatic water metering technology, nodal water demands can be modeled with high time resolution in certain forms of probability distributions. However, the fusion of various demand probability distributions with conventional measurements to improve the accuracy of WDS hydraulic models is a difficult problem. To resolve this, a numerical approach that incorporates various probability distributions and field measurements to calibrate nodal water demands based on Bayesian theory is proposed. In particular, the linearization of the exponential family prior distribution is well elaborated in this paper. The application of this proposed approach in two cases demonstrates that the technique is more accurate than methods that merely utilize measurements or prior information. Because this technique can avoid the overfitting of measurement noise and allow the retention of calibrated nodal water demands with stochastic nature, it is robust when errors or uncertainties exist in prior demand distribution or measurements. This method is expected to improve the WDS model accuracy relative to the increasing use of automatic water metering technology.

Keywords: Automatic water meter; Bayesian framework; Prior information; Real-time.